Reading the Ancient Compass
Every paleomagnetic measurement produces two angles: declination (the compass direction of the ancient field) and inclination (the dip angle below horizontal). Together, these define a unit vector pointing in the direction of the geomagnetic field at the time and place the rock acquired its magnetization. Plotting these directions on a stereographic projection — the paleomagnetist's essential diagram — reveals patterns invisible in raw numbers.
The Stereographic Projection
The equal-angle stereographic projection maps the lower hemisphere of directions onto a circle. Declination controls the azimuthal position (0° = north, 90° = east), while inclination controls the radial distance from the center (90° at center, 0° at the rim). This projection preserves angular relationships, making it ideal for assessing directional clustering, identifying multiple magnetization components, and displaying statistical confidence cones.
Fisher Statistics
Paleomagnetic directions are analyzed using Fisher (1953) statistics — the spherical analogue of Gaussian statistics for linear data. The precision parameter κ measures concentration (higher = tighter clustering), and α95 gives the cone of 95% confidence around the mean. A well-determined paleomagnetic direction typically has κ > 50 and α95 < 5°. The mean direction and its confidence cone are the primary results reported from any paleomagnetic study.
From Directions to Continents
The dipole formula tan I = 2 tan λ converts measured inclination to paleolatitude — the latitude of the site when the rock formed. Combined with declination (which gives the azimuthal orientation of the continent relative to the pole), paleomagnetic directions provide two of the three Euler rotation parameters needed to reconstruct past continental positions. This is why paleomagnetism remains the only quantitative method for positioning continents in deep geological time.